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Integrable slowly varying function

We say a function $L$ is slowly varying if $$\lim_{t\to\infty} \frac{L(tx)}{L(t)} = 1$$ for every $x > 0$. Are there such $L$ that are integrable? Say $L$ is defined on $[0,\infty)$ and is ...
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Sums of partially dependent Bernoulli random variables

I am looking for any kind of Chernoff type large deviation bound for the following random variable: $$X = \sum_{i=1}^NX_i$$ where each $X_i$ is an identically distributed Bernoulli random variable ...
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Tail bounds of reciprocals

Suppose one knows that for a random function $f(n)$, $f(n)-a$ decays at some rate given by: $$Pr(|f(n)-t|>\epsilon)=g(\epsilon),$$for $g(\epsilon)\to0$, all as $n\to\infty$. If the above holds, ...
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Scaling Cumulative Probability Distribution function values

We have a cumulative probability distribution function (cdf), we want to scale it down for using it in anomaly detection. The mapping should look like this. CDF value: 0.1 ... 0.5 ... 0.9 ... ...
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